Space of modular forms of level 546, weight 4, and Character 546.p

• Label: 546.4.p
• Level: $546$
• Weight: $4$
• Character orbit: 546.p
• Rep. character: $\chi_{546}(239,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $168$
• Sturm bound: $448$

Defining parameters

Level:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	546.p (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 39 \)
Character field:			\(\Q(i)\)
Sturm bound:			\(448\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(546, [\chi])\).

	Total	New	Old
Modular forms	688	168	520
Cusp forms	656	168	488
Eisenstein series	32	0	32

Trace form

168 * q - 240 * q^13 - 168 * q^15 - 2688 * q^16 - 16 * q^18 - 96 * q^19 - 224 * q^21 - 1248 * q^27 - 432 * q^31 + 600 * q^33 + 1344 * q^34 - 528 * q^37 + 1520 * q^39 + 664 * q^45 - 528 * q^46 - 96 * q^54 - 1248 * q^55 + 656 * q^57 - 2160 * q^58 - 672 * q^60 + 1248 * q^61 - 1064 * q^63 - 1984 * q^66 - 216 * q^67 - 64 * q^72 - 2928 * q^73 - 384 * q^76 - 544 * q^78 + 12432 * q^79 + 5952 * q^81 + 896 * q^84 - 12336 * q^85 - 840 * q^91 - 1656 * q^93 - 480 * q^94 - 8256 * q^97 + 752 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(546, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{4}^{\mathrm{old}}(546, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(546, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(78, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(273, [\chi])\)\(^{\oplus 2}\)